Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2024 Nov 29;14(1):29728.
doi: 10.1038/s41598-024-81075-w.

A multi-level thresholding image segmentation algorithm based on equilibrium optimizer

Pei Hu  1 , Yibo Han  1 , Zheng Zhang  1 , Shu-Chuan Chu  2 , Jeng-Shyang Pan  3   4
Affiliations

A multi-level thresholding image segmentation algorithm based on equilibrium optimizer

Pei Hu et al. Sci Rep. .

Abstract

Multi-level thresholding for image segmentation is one of the key techniques in image processing. Although numerous methods have been introduced, it remains challenging to achieve stable and satisfactory thresholds when segmenting images with various unknown properties. This paper proposes an equilibrium optimizer algorithm to find the optimal multi-level thresholds for grayscale images. The proposed algorithm AEO (advanced equilibrium optimizer) uses two sub-populations to balance exploration and exploitation during the multi-level threshold search process. Two mutation schemes are proposed for the sub-populations to prevent them from being trapped in local optima. AEO offers a repair function to avoid generating duplicate thresholds. The performance of AEO is evaluated on multiple benchmark images. Experimental results demonstrate that AEO has an outstanding ability for multi-level threshold image segmentation in terms of cross-entropy, signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and feature similarity index (FSIM).

Keywords: Equilibrium optimizer; Image segmentation; Multi-level thresholding.

PubMed Disclaimer

Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

Figures

Figure 1
Figure 1
The image segmentation process.
Algorithm 1
Algorithm 1
AEO
Algorithm 2
Algorithm 2
Mutation1
Algorithm 3
Algorithm 3
Mutation2
Figure 2
Figure 2
The examples of the proposed mutations.
Algorithm 4
Algorithm 4
Repairing operation
Figure 3
Figure 3
The examples of the proposed repairing method.
See this image and copyright information in PMC

References

    1. Huang, T., Yin, H. & Huang, X. Improved genetic algorithm for multi-threshold optimization in digital pathology image segmentation. Sci. Rep.14, 22454 (2024). - PMC - PubMed
    1. Hossain, S., Mukhopadhyay, S., Ray, B., Ghosal, S. K. & Sarkar, R. A secured image steganography method based on ballot transform and genetic algorithm. Multimed. Tools Appl.81, 38429–38458 (2022).
    1. Nie, F., Liu, M. & Zhang, P. Multilevel thresholding with divergence measure and improved particle swarm optimization algorithm for crack image segmentation. Sci. Rep.14, 7642 (2024). - PMC - PubMed
    1. Sun, G., Zhang, A., Yao, Y. & Wang, Z. A novel hybrid algorithm of gravitational search algorithm with genetic algorithm for multi-level thresholding. Appl. Soft Comput.46, 703–730. 10.1016/j.asoc.2016.01.054 (2016).
    1. Mukhopadhyay, S., Hossain, S., Ghosal, S. K. & Sarkar, R. Secured image steganography based on Catalan transform. Multimed. Tools Appl.80, 14495–14520 (2021).

LinkOut - more resources